When you meet her at Hysteria Hall, choose the Voigt-Kampff conversation option. She'll run off into the maze, so you need to follow her. Inside the maze you can shoot her, but it's not easy to get close to her with the moving walls. I can't remember exactly, but I think I did it something like this :

- A wall will move in the bottom-left corner so you can't follow Lucy
- Stay were you are instead of following the alternate route
- The wall in the bottom-left corner will move again so you can now follow this route.
- Lucy ran too far to leave the maze, she should be in the top-right corner and has to run back.
- Run quickly to the middle-right where she needs to pass to reach the exit
- Shoot her when she passes

"Yeah, I’ve seen the data. Implanted memories and four year life span. I’d probably get a little crazy too, but I wouldn’t start killing people."